Answer:
Step-by-step explanation:
The set {1,2,3,4,5,6} has a total of 6! permutations
a. Of those 6! permutations, 5!=120 begin with 1. So first 120 numbers would contain 1 as the unit digit.
b. The next 120, including the 124th, would begin with '2'
c. Then of the 5! numbers beginning with 2, there are 4!=24 including the 124th number, which have the second digit =1
d. Of these 4! permutations beginning with 21, there are 3!=6 including the 124th permutation which have third digit 3
e. Among these 3! permutations beginning with 213, there are 2 numbers with the fourth digit =4 (121th & 122th), 2 with fourth digit 5 (numbers 123 & 124) and 2 with fourth digit 6 (numbers 125 and 126).
Lastly, of the 2! permutations beginning with 2135, there is one with 5th digit 4 (number 123) and one with 5 digit 6 (number 124).
∴ The 124th number is 213564
Similarly reversing the above procedure we can determine the position of 321546 to be 267th on the list.
Answer: (B)
Explanation: If you are unsure about where to start, you could always plot some numbers down until you see a general pattern.
But a more intuitive way is to determine what happens during each transformation.
A regular y = |x| will have its vertex at the origin, because nothing is changed for a y = |x| graph. We have a ray that is reflected at the origin about the y-axis.
Now, let's explore the different transformations for an absolute value graph by taking a y = |x + h| graph.
What happens to the graph?
Well, we have shifted the graph -h units, just like a normal trigonometric, linear, or even parabolic graph. That is, we have shifted the graph h units to its negative side (to the left).
What about the y = |x| + h graph?
Well, like a parabola, we shift it h units upwards, and if h is negative, we shift it h units downwards.
So, if you understand what each transformation does, then you would be able to identify the changes in the shape's location.
Answer:
1. 64
2. 72 square feet
3. 31.5 square feet
Step-by-step explanation:
For the first one use the equation A=bh.
Plug in your values: A=12.8*5.
Solve: A=64
For the second one multiply 8*3 which gives you 24. Next multiply that by 3 to give you 72 square feet.
For the third one multiply 9 by 3.5 to get 31.5 square feet.
Answer:
Well if (a,b) is in Quadrant IV which is the last quadrant the a or x is a positive number and the b or y is a negative number.
